Question

what is improper integral?

Answer 1

An integral which is specifically between two points as opposed to just a general form of an integral.

Answer 2

an improper integral has at least part of the function domain undefined or infinite
examples\[\int_a^\infty f(x)dx\]\[\int_{-\infty}^ b f(x)dx\]\[\int_{-\infty}^\infty f(x)dx\]or any time there is a singularity within the bounds of integration, like\[\int_{-1}^1\frac{dx}x\]since 1/x is undefined at x=0 this is also an improper integral